Prolog, check divisibility in Peano arithmetic

Question

I need to check if first given term (for example s(s(nul)) (or 2)) is dividable by the second term, (for example s(nul) (or 1)).

What I want to do is multiply given term by two and then check if that term is smaller or equal to the other term (if it is equal - problem is solved).

So far I got this:

checkingIfDividable(X,X).
checkingIfDividable(X,Y) :-
    X > Y,
    multiplication(X,Y).

/* multiplication by two should occur here. 
   I can't figure it out. This solution does not work!*/
multiplication(Y):-
    YY is Y * 2,
    checkingIfDividable(X,YY).

I can't seem to figure out how to multiply a term by 2. Any ideas?

Answer 1

If a = n*b, n > 0, it is also a = n*b = (1+m)*b = b + m*b, m >= 0.

So if a is dividable by b, and a = b+x, then x is also dividable by b.

In Peano encoding, n = 1+m is written n = s(m).

Take it from here.